On multiplier weighted-space of sequences
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We consider the weighted spaces $\ell ^{p}(\mathbb{S},\varphi )$ and $\ell ^{p}(\mathbb{S},\psi )$ for $1<p<+\infty ,$ where $\varphi $ and $\psi $ are weights on $\mathbb{S}$ $\mathbb{(=N}$ or $\mathbb{Z)}$. We obtain a sufficient condition for $\ell ^{p}(\mathbb{S},\psi )$ to be multiplier weighted-space of $\ell ^{p}(\mathbb{S},\varphi )$ and $\ell ^{p}( \mathbb{S},\psi )$. Our condition characterizes the last multiplier weighted-space in the case where $\mathbb{S=Z}$. As a consequence, in the particular case where $\psi =\varphi $, the weighted space $\ell ^{p}( \mathbb{Z}$,$\psi )$ is a convolutive algebra.
Abstract
We consider the weighted spaces $\ell ^{p}(\mathbb{S},\varphi )$ and $\ell ^{p}(\mathbb{S},\psi )$ for $1<p<+\infty ,$ where $\varphi $ and $\psi $ are weights on $\mathbb{S}$ $\mathbb{(=N}$ or $\mathbb{Z)}$. We obtain a sufficient condition for $\ell ^{p}(\mathbb{S},\psi )$ to be multiplier weighted-space of $\ell ^{p}(\mathbb{S},\varphi )$ and $\ell ^{p}( \mathbb{S},\psi )$. Our condition characterizes the last multiplier weighted-space in the case where $\mathbb{S=Z}$. As a consequence, in the particular case where $\psi =\varphi $, the weighted space $\ell ^{p}( \mathbb{Z}$,$\psi )$ is a convolutive algebra.
참고문헌 (5)
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